You can restore hard plastics, such as acrylic and polycarbonate, by sanding them, and the procedure is similar to sanding a wood finish. Because plastic scratches easily, coarse sandpaper grits aren't recommended. The best strategy is to begin wet sanding with 220-grit sandpaper and make additional passes with progressively finer paper until you're happy with the appearance.
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Wet Sanding Technique
The type of sandpaper you need for wet sanding is called silicon carbide -- or wet/dry -- sandpaper. It's usually black or gray. Immerse the paper in water for 10 minutes, then sand in a circular motion. Keep the sanding pattern irregular to avoid producing deep scratches that might remain visible. Using a foam block to support the sandpaper is helpful when sanding curved surfaces, such as headlight lenses.
A Typical Procedure
Before sanding, clean off dirt and grime with a mild detergent solution. Use a 50/50 solution of vinegar and water to clean extensively pitted plastic, because vinegar is a weak acid, and it helps smooth the surface. Run through the sanding grits in order from 220- to 400-, 800- and 1,200-grit, finishing with 1,500- or 2,000-grit, depending on how smooth you want the surface. Clean sanding residue with water after you're done with each grit. To get the maximum sheen, spread automotive clear-coat polishing compound on the surface and buff it with a lambswool buffer.